UA mainline has around 130-150 flights daily. (Compared to about 70-80 on US.) UA Express (ACA really) is the biggie with over 250 flights a day... if you like J31s and J42s. Sure, they have RJs, but not so many of the flights are on them as on the puddlejumpers.
I disagree with the idea that IAD could relieve ORD. They are nearly 600 miles apart, and definitely service different markets. As you said, IAD could make an impressive East Coast N/S hub if UA ever got off their duff and made it so. But, it isn't so hot for E/W as it is too far east. No one likes flying east to get west. ORD is the mother of all E/W hubs, and obviously doesn't have that problem. (Possibly the only problem it doesn't have.
The two airports are very complementary.
To pick apart my own argument a bit, there are definite advantages to keeping as few hubs as possible, and concentrating everything at select hubs. The more flights landing and taking off an hour later, the larger your 'bank' is. A large bank of flights means that even the smallest of cities are given a very large number of destinations.
PIT would obviously suffer in a merger with UA (or AA for that matter) if not for the fact that ORD is full. PHL, IAD and CLT could survive harmoniously because of the density of the areas they serve. Remember, nobody wants to fly north to get south. DC Area folks will not like to connect in Philly to get to Florida. Philly Area folks will not like to connect in DC to get to Europe, etc. There are enough people imo living in this area that eliminating one of the three hubs would be a major annoyance, and would eat away at the customer base and route network that makes US so profitable.